Twitter is stepping up its legal battle for users’ privacy: First it fought to reveal secret warrantless law enforcement requests for its users’ data. Now it’s fighting to block one such request altogether.

In a motion (PDF here) filed yesterday in a New York state court, Twitter asked a judge to block a subpoena that would force the company to turn over the data of Malcolm Harris, a participant in the Occupy Wall Street protests who was arrested in a demonstration on the Brooklyn Bridge in October for “disorderly conduct.”

The prosecutors in the case have sent Twitter what’s known as a 2703 order, which allows prosecutors to access some types of a user’s data without a warrant under the Stored Communications Act (SCA).

In its motion, Twitter offers three arguments against turning over that data: First, that the data belongs to Harris under Twitter’s terms of service, and handing it over would violate both those terms of service and the SCA. Second, it argues that handing over Harris’s data would violate the Fourth Amendment’s protections against searches without a warrant, which it argues applies even when the government is seeking information about allegedly public activities like a user’s tweets. And third, it points out that Twitter is in California, and argues that the New York prosecutors need to make their case to a California court to obtain Twitter’s data.

Twitter’s bold legal move isn’t the first time it’s taken a stand against warrantless requests for its data. In January of 2011 it revealed to three associates of WikiLeaks that their data had been sought in a secret grand jury investigation. (Other services like Google and Facebook were likely subpoenaed as well, without notifying the WikiLeakers.) And earlier this year it notified Harris of the subpoena for his data. He fought the order, but lost on the grounds that the data being sought was held by Twitter, not Harris.

That’s why Twitter’s move to fight the subpoena is “a big deal,” as ACLU attorney Aden Fine has written in a blog post. “Law enforcement agencies—both the federal government and state and city entities—are becoming increasingly aggressive in their attempts to obtain information about what people are doing on the Internet. And while the individual Internet users can try to defend their rights in the rare circumstances in which they find out about the requests before their information is turned over, that may not be enough…If Internet users cannot protect their own constitutional rights, the only hope is that Internet companies do so.”

Just what prosecutors hope to get from Harris’s Twitter records isn’t exactly clear. In the ruling that denied Harris’s own motion to block the subpoena of his Twitter information, prosecutors wrote that “the information sought by the subpoena is needed to refute the defendant’s anticipated defense, that the police either led or escorted the defendant onto stepping onto the roadway of the Brooklyn Bridge.” It’s worth noting that all of Harris’s data, including private direct messages and deleted tweets, would likely be included in the subpoena.

Harris has deleted all public tweets before February, and has told Gawker that he had no idea what the prosecutors were looking for. In a March message, he wrote that the case “is [the] legal equivalent of busting a party with loud noise and demanding my phone records for 3.5 months to see if I helped plan it.”